Not that there is anything wrong with giving the baby her last name....it's actually not the baby's last name -- per celebritybabyblog.com -- http://www.celebrity-babies.com/2008/03/giada-de-lauren.html -- the babies last name is Thompson and 'De Laurentiis' is her second middle name.
Scroll down on the page to the comments and in the bolded part (the moderator's comments) it says: "Sarah's note: No, it's a second middle name. Giada said in Feb that the last name is just Thompson."